The first solution you describe is the best if you want to maintain data integrity, and if you have relatively few product types and seldom add new product types. This is the design I'd choose in your situation. Reporting is complex only if your reports need the product-specific attributes. If your reports need only the attributes in the common Products table, it's fine.
The second solution you describe is called "Polymorphic Associations" and it's no good. Your "foreign key" isn't a real foreign key, so you can't use a DRI constraint to ensure data integrity. OO polymorphism doesn't have an analog in the relational model.
The third solution you describe, involving storing an attribute name as a string, is a design called "Entity-Attribute-Value" and you can tell this is a painful and expensive solution. There's no way to ensure data integrity, no way to make one attribute NOT NULL, no way to make sure a given product has a certain set of attributes. No way to restrict one attribute against a lookup table. Many types of aggregate queries become impossible to do in SQL, so you have to write lots of application code to do reports. Use the EAV design only if you must, for instance if you have an unlimited number of product types, the list of attributes may be different on every row, and your schema must accommodate new product types frequently, without code or schema changes.
Another solution is "Single-Table Inheritance." This uses an extremely wide table with a column for every attribute of every product. Leave NULLs in columns that are irrelevant to the product on a given row. This effectively means you can't declare an attribute as NOT NULL (unless it's in the group common to all products). Also, most RDBMS products have a limit on the number of columns in a single table, or the overall width in bytes of a row. So you're limited in the number of product types you can represent this way.
Hybrid solutions exist, for instance you can store common attributes normally, in columns, but product-specific attributes in an Entity-Attribute-Value table. Or you could store product-specific attributes in some other structured way, like XML or YAML, in a BLOB column of the Products table. But these hybrid solutions suffer because now some attributes must be fetched in a different way
The ultimate solution for situations like this is to use a semantic data model, using RDF instead of a relational database. This shares some characteristics with EAV but it's much more ambitious. All metadata is stored in the same way as data, so every object is self-describing and you can query the list of attributes for a given product just as you would query data. Special products exist, such as Jena or Sesame, implementing this data model and a special query language that is different than SQL.